Question

In: Statistics and Probability

Suppose that the probability that any random student graduates with honors is 0.05. Also, we know...

Suppose that the probability that any random student graduates with honors is 0.05. Also, we know that the probability of a student that graduated with honors, getting into graduate school is 0.80. The probability that a student that did not graduate with honors gets into graduate school is 0.10. TRUE or FALSE: Given that a random student got into graduate school, it is more likely that the student graduated with honors.

True

False

Solutions

Expert Solution

P(graduates with honors) = 0.05

P(gets into graduate school | graduated with honors) = 0.8

P(gets into graduate school | didn't graduate with honors) = 0.1

P(gets into graduate school) = P(gets into graduate school | graduated with honors) * P(graduated with honors) + P(gets into graduate school | didn't graduate with honors) * P( didn't graduate with honors)

                                              = 0.8 * 0.05 + 0.1 * (1 - 0.05)

                                              = 0.135

P(graduated with honors | got into graduate school) = P(gets into graduate school | graduated with honors) * P(graduated with honors) / P(gets into graduate school)

                                                   = 0.8 * 0.05 / 0.135

                                                   = 0.296

Option-B) False. Becase thi probability is less than 0.5

orchestra answered 1 year ago
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